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On Non-Integral Dehn Surgeries Creating Non-Orientable Surfaces

Published:2006-12-01
Printed: Dec 2006
• Masakazu Teragaito
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Abstract

For a non-trivial knot in the $3$-sphere, only integral Dehn surgery can create a closed $3$-manifold containing a projective plane. If we restrict ourselves to hyperbolic knots, the corresponding claim for a Klein bottle is still true. In contrast to these, we show that non-integral surgery on a hyperbolic knot can create a closed non-orientable surface of any genus greater than two.
 Keywords: knot, Dehn surgery, non-orientable surface
 MSC Classifications: 57M25 - Knots and links in $S^3$ {For higher dimensions, see 57Q45}